It's more or less impossible to shade a space elevator because the (hot, radiant) earth spans a full hemisphere of its field of view and the sun wanders most of the opposite one.
No way to passively reach cryogenic temperatures—let alone the deep-cryogenic ones demanded by high current-density superconductors.
No way to passively reach cryogenic temperatures—let alone the deep-cryogenic ones demanded by high current-density superconductors.